Geodesic
Correction theorem for Sobolev spaces constructed by a~symmetric space
Informatics and Automation, Function spaces and related problems of analysis, Tome 284 (2014), pp. 38-55

Voir la notice de l'article provenant de la source Math-Net.Ru

A sharp correction theorem is established for Sobolev spaces in which the norm (quasinorm) of generalized derivatives is calculated in an arbitrary symmetric space. The exact relation between the norm of a corrected function in the Lipschitz space and the measure of the set on which the corrected and original functions are different makes it possible to characterize the Sobolev spaces constructed on the basis of the Marcinkiewicz space in terms of correctability. This opens a way to constructing Sobolev–Marcinkiewicz spaces for functions with an arbitrary domain of definition. 
@article{TRSPY_2014_284_a2,
     author = {E. I. Berezhnoi},
     title = {Correction theorem for {Sobolev} spaces constructed by a~symmetric space},
     journal = {Informatics and Automation},
     pages = {38--55},
     publisher = {mathdoc},
     volume = {284},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2014_284_a2/}
}
TY  - JOUR
AU  - E. I. Berezhnoi
TI  - Correction theorem for Sobolev spaces constructed by a~symmetric space
JO  - Informatics and Automation
PY  - 2014
SP  - 38
EP  - 55
VL  - 284
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2014_284_a2/
LA  - ru
ID  - TRSPY_2014_284_a2
ER  - 
%0 Journal Article
%A E. I. Berezhnoi
%T Correction theorem for Sobolev spaces constructed by a~symmetric space
%J Informatics and Automation
%D 2014
%P 38-55
%V 284
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2014_284_a2/
%G ru
%F TRSPY_2014_284_a2
E. I. Berezhnoi. Correction theorem for Sobolev spaces constructed by a~symmetric space. Informatics and Automation, Function spaces and related problems of analysis, Tome 284 (2014), pp. 38-55. http://geodesic.mathdoc.fr/item/TRSPY_2014_284_a2/